In the case of performing an engine control or an exhaust gas purification control of a vehicle, in order to improve the accuracy of the control, it is important to exactly understand the property of each part of the engine. Particularly, an exhaust gas temperature in an exhaust manifold is very important. In the case of using a general thermistor type temperature sensor in order to detect the exhaust gas temperature, if the protruding amount of the sensor into the exhaust manifold increases (especially, the protruding amount of the sensor increases in the case of a large diesel engine having an exhaust manifold of a large diameter), there is a danger that the sensor may be broken by an engine vibration or an exhaust vibration. If the diameter of the sensor is increased as a countermeasure against the breakage, the sensor has a low responsiveness which is improper for the control. Therefore, there are technologies of estimating an exhaust gas temperature using detected values of sensors disposed at other locations of the engine without using the above-mentioned sensor. Patent Literature 1 discloses a technology of detecting an intra-cylinder pressure by an intra-cylinder pressure sensor installed at a cylinder of an engine and estimating the temperature of the exhaust gas side based on the detected value. Further, Patent Literature 2 discloses a technology of measuring the number of revolutions or a load of an engine, obtaining a standard exhaust gas temperature from an exhaust gas temperature map by using the measured values, and modifying the standard exhaust gas temperature by means of an atmospheric pressure and an intake temperature, so as to estimate the exhaust gas temperature.